How do I change my RDS Postgres engine version from the AWS console?

Hi, @Shorn.

Can you share a screenshot of the management console?
Normally you should be able to select the new engine version.

When I came back the next day (this morning) - the console now has the DB engine version options I expected.

Over the course of trying to diagnose the issue yesterday, I took a lot of different actions, so I've no idea what (if any) caused the problem to go away. I tried to post my notes here but they're too long and I'm not willing to spend time editing them for this forum.